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3 years ago

11

A washer and a dryer cost $1000 combined. The cost of the washer is $175 more than the cost of the dryer. Determine the cost of

the washer and the cost of the dryer.

1 answer:

kifflom [539]3 years ago

7 0

Answer:

washer is 587$

Step-by-step explanation:

1000 - 175

825

825 divided by 2 than add 175 to the washers half

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What radical expression is not simplified?

rodikova [14]

B 2/10 is not simplified because you can divide each number by 2 reducing it to 1/5.

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3 years ago

Marine biologists have determined that when a shark detectsthe presence of blood in the water, it will swim in the directionin w

siniylev [52]

Solution :

a). The level curves of the function :

$C(x,y) = e^{-(x^2+2y^2)/10^4}$

are actually the curves

$e^{-(x^2+2y^2)/10^4}=k$

where k is a positive constant.

The equation is equivalent to

$x^2+2y^2=K$

$\Rightarrow \frac{x^2}{(\sqrt K)^2}+\frac{y^2}{(\sqrt {K/2})^2}=1, \text{ where}\ K = -10^4 \ln k$

which is a family of ellipses.

We sketch the level curves for K =1,2,3 and 4.

If the shark always swim in the direction of maximum increase of blood concentration, its direction at any point would coincide with the gradient vector.

Then we know the shark's path is perpendicular to the level curves it intersects.

b). We have :

$\triangledown C= \frac{\partial C}{\partial x}i+\frac{\partial C}{\partial y}j$

$\Rightarrow \triangledown C =-\frac{2}{10^4}e^{-(x^2+2y^2)/10^4}(xi+2yj),$ and

$\triangledown C$ points in the direction of most rapid increase in concentration, which means $\triangledown C$ is tangent to the most rapid increase curve.

$r(t)=x(t)i+y(t)j$ is a parametrization of the most $\text{rapid increase curve}$ , then

$\frac{dx}{dt}=\frac{dx}{dt}i+\frac{dy}{dt}j$ is a tangent to the curve.

So then we have that $\frac{dr}{dt}=\lambda \triangledown C$

$\Rightarrow \frac{dx}{dt}=-\frac{2\lambda x}{10^4}e^{-(x^2+2y^2)/10^4}, \frac{dy}{dt}=-\frac{4\lambda y}{10^4}e^{-(x^2+2y^2)/10^4}$

∴ $\frac{dy}{dx}=\frac{dy/dt}{dx/dt}=\frac{2y}{x}$

Using separation of variables,

$\frac{dy}{y}=2\frac{dx}{x}$

$\int\frac{dy}{y}=2\int \frac{dx}{x}$

$\ln y=2 \ln x$

⇒ y = kx^2 for some constant k

but we know that $y(x_0)=y_0$

$\Rightarrow kx_0^2=y_0$

$\Rightarrow k =\frac{y_0}{x_0^2}$

∴ The path of the shark will follow is along the parabola

$y=\frac{y_0}{x_0^2}x^2$

$y=y_0\left(\frac{x}{x_0}\right)^2$

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2 years ago

Dan invests £8000 into his bank account.

Serhud [2]

If 8000 dollars multiplied by 2% is 160 dollars and 160 dollars multiplied by 3 years gives you the answer of 480 dollars

6 0

3 years ago

Read 2 more answers

Triangle ABC has been reflected over the x-axis to create triangle A'B'C'. Which of the following statements is true?

Leto [7]

Answer:

A ' = (-2, -3)

B ' = (0, -3)

C ' = (-1, 1)

=======================================================

Explanation:

To apply an x axis reflection, we simply change the sign of the y coordinate from positive to negative, or vice versa. The x coordinate stays as is.

Algebraically, the reflection rule used can be written as

Applying this rule to the three given points will mean....

Point A = (-2, 3) becomes A ' = (-2, -3)

Point B = (0, 3) becomes B ' = (0, -3)

Point C = (-1, -1) becomes C ' = (-1, 1)

The diagram is provided below.

Side note: Any points on the x axis will stay where they are. That isn't the case here, but its for any future problem where it may come up. This only applies to x axis reflections.

Step-by-step explanation:

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2 years ago

Order these numbers from Least to Greatest 4,209 2,438 4,703 3,026

Virty [35]

2,438 3,026 4,209 4,703

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3 years ago